In this section we present the proofs of stability (Theorem ) and diminishing queueing probability (Theorem ). Since the structure of our proofs is similar in spirit to that of the recently-developed drift method [1]}, [2]}, [3]}, we first provide some background on the drift method in Section REF . We then sketch our approach in Section REF  and highlight how it deviates from the traditional drift method. Finally, we present the detailed proofs in Section REF .
